diff --git a/404.html b/404.html
index f0763b8..179b287 100644
--- a/404.html
+++ b/404.html
@@ -376,8 +376,8 @@ <h1>Page not found</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/404.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/404.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/CODE_OF_CONDUCT.html b/CODE_OF_CONDUCT.html
index bf94f27..3d063ad 100644
--- a/CODE_OF_CONDUCT.html
+++ b/CODE_OF_CONDUCT.html
@@ -399,7 +399,7 @@ <h1>Contributor Code of Conduct</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/CODE_OF_CONDUCT.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-09-24",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/LICENSE.html b/LICENSE.html
index f62d7b2..17e9ce8 100644
--- a/LICENSE.html
+++ b/LICENSE.html
@@ -447,7 +447,7 @@ <h1>Licenses</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/LICENSE.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-09-24",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/aio.html b/aio.html
index 39ebf50..f45d2bb 100644
--- a/aio.html
+++ b/aio.html
@@ -2734,7 +2734,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <p>We see in the help documentation for <code>?clusterCells</code> that
 all of the clustering algorithm details are handled through the
@@ -2931,7 +2931,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <p>You can see that at least among the top markers, cluster 6 (pale
 green) tends to have the least separation from cluster 1.</p>
@@ -3229,7 +3229,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -3493,7 +3493,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb43">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -3643,7 +3643,7 @@ <h3 class="callout-title">Exercise 1: Clustering</h3>
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>The <code>NNGraphParam</code> constructor has an argument
 <code>cluster.args</code>. This allows to specify arguments passed on to
@@ -3660,7 +3660,7 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
   <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
+<div id="collapseSolution5" class="accordion-collapse collapse" data-bs-parent="#accordionSolution5" aria-labelledby="headingSolution5">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -3699,7 +3699,7 @@ <h3 class="callout-title">Exercise 2: Reference marker genes</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution6" aria-expanded="false" aria-controls="collapseSolution6">
   <h4 class="accordion-header" id="headingSolution6"> Show me the solution </h4>
 </button>
-<div id="collapseSolution6" class="accordion-collapse collapse" aria-labelledby="headingSolution6" data-bs-parent="#accordionSolution6">
+<div id="collapseSolution6" class="accordion-collapse collapse" data-bs-parent="#accordionSolution6" aria-labelledby="headingSolution6">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb47">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -3772,7 +3772,7 @@ <h3 class="callout-title">Extension Challenge 1: Group pair comparisons</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution7" aria-expanded="false" aria-controls="collapseSolution7">
   <h4 class="accordion-header" id="headingSolution7"> Show me the solution </h4>
 </button>
-<div id="collapseSolution7" class="accordion-collapse collapse" aria-labelledby="headingSolution7" data-bs-parent="#accordionSolution7">
+<div id="collapseSolution7" class="accordion-collapse collapse" data-bs-parent="#accordionSolution7" aria-labelledby="headingSolution7">
 <div class="accordion-body">
 <p>One important reason why is because averages over all other clusters
 can be sensitive to the cell type composition. If a rare cell type shows
@@ -3806,7 +3806,7 @@ <h3 class="callout-title">Extension Challenge 2: Parallelizing SingleR</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution8" aria-expanded="false" aria-controls="collapseSolution8">
   <h4 class="accordion-header" id="headingSolution8"> Show me the solution </h4>
 </button>
-<div id="collapseSolution8" class="accordion-collapse collapse" aria-labelledby="headingSolution8" data-bs-parent="#accordionSolution8">
+<div id="collapseSolution8" class="accordion-collapse collapse" data-bs-parent="#accordionSolution8" aria-labelledby="headingSolution8">
 <div class="accordion-body">
 <p>Use <code>BiocParallel</code> and the <code>BPPARAM</code> argument!
 This example will set it to use four cores on your laptop, but you can
@@ -3848,7 +3848,7 @@ <h3 class="callout-title">Extension Challenge 3: Critical inspection of diagnost
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution9" aria-expanded="false" aria-controls="collapseSolution9">
   <h4 class="accordion-header" id="headingSolution9"> Show me the solution </h4>
 </button>
-<div id="collapseSolution9" class="accordion-collapse collapse" aria-labelledby="headingSolution9" data-bs-parent="#accordionSolution9">
+<div id="collapseSolution9" class="accordion-collapse collapse" data-bs-parent="#accordionSolution9" aria-labelledby="headingSolution9">
 <div class="accordion-body">
 <p>The example that jumps out most strongly to the eye is ExE endoderm,
 which doesn’t show clear separate modes. Simultaneously, Endothelium
@@ -3927,7 +3927,7 @@ <h3 class="callout-title">Key Points</h3>
  -->
 </section></section><section id="aio-multi-sample"><p>Content from <a href="multi-sample.html">Multi-sample analyses</a></p>
 <hr>
-<p>Last updated on 2024-10-03 |
+<p>Last updated on 2024-10-04 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 <div class="text-end">
@@ -4968,16 +4968,15 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </section><section><h2 class="section-heading" id="exercises">Exercises<a class="anchor" aria-label="anchor" href="#exercises"></a>
 </h2>
 <hr class="half-width">
-<div id="exercise-1-replicates" class="callout challenge">
+<div id="exercise-1-heatmaps" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-1-replicates" class="callout-inner">
-<h3 class="callout-title">Exercise 1: Replicates</h3>
+<div id="exercise-1-heatmaps" class="callout-inner">
+<h3 class="callout-title">Exercise 1: Heatmaps</h3>
 <div class="callout-content">
-<p>Test differential expressed genes with just 2 replicates per
-condition and look into the changes in the results and possible emerging
-issues.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -4988,9 +4987,9 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
-<p>Remember, you can subset SingleCellExperiments with logical indices,
-just like a matrix. You can also access their column data with the
-<code>$</code> accessor, like a data frame.</p>
+<p>You can simply hand <code>pheatmap()</code> a matrix as its only
+argument. <code>pheatmap()</code> has a million options you can tweak,
+but the defaults are usually pretty good.</p>
 </div>
 </div>
 </div>
@@ -5006,29 +5005,27 @@ <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
-<span></span>
-<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
-<span>    <span class="va">summed.filt.subset</span>, </span>
-<span>    label <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
-<span>    design <span class="op">=</span> <span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
-<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
-<span>    condition <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
-<span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
 </div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-24-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-heatmaps" class="callout challenge">
+<div id="exercise-2-model-specification-and-comparison" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-heatmaps" class="callout-inner">
-<h3 class="callout-title">Exercise 2: Heatmaps</h3>
+<div id="exercise-2-model-specification-and-comparison" class="callout-inner">
+<h3 class="callout-title">Exercise 2: Model specification and comparison</h3>
 <div class="callout-content">
-<p>Use the <code>pheatmap</code> package to create a heatmap of the
-abundances table. Does it comport with the model results?</p>
+<p>Try re-running the pseudobulk DGE without the <code>pool</code>
+factor in the design specification. Compare the logFC estimates and the
+distribution of p-values for the <code>Erythroid3</code> cell type.</p>
 </div>
 </div>
 </div>
@@ -5039,9 +5036,10 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" data-bs-parent="#accordionHint2" aria-labelledby="headingHint2">
 <div class="accordion-body">
-<p>You can just hand <code>pheatmap()</code> a matrix as its only
-argument. It has a million options, but the defaults are usually pretty
-good.</p>
+<p>After running the second pseudobulk DGE, you can join the two
+<code>DataFrame</code>s of <code>Erythroid3</code> statistics using the
+<code>merge()</code> function. You will need to create a common key
+column from the gene IDs.</p>
 </div>
 </div>
 </div>
@@ -5057,13 +5055,61 @@ <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="va">de.results2</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
+<span>    <span class="va">summed.filt</span>, </span>
+<span>    label <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design <span class="op">=</span> <span class="op">~</span><span class="va">tomato</span>,</span>
+<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth1</span> <span class="op">&lt;-</span> <span class="va">de.results</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth2</span> <span class="op">&lt;-</span> <span class="va">de.results2</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth1</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth1</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth2</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth2</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="fu">merge</span><span class="op">(</span><span class="va">eryth1</span>, <span class="va">eryth2</span>, by <span class="op">=</span> <span class="st">'gene'</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="va">comp_df</span><span class="op">[</span><span class="op">!</span><span class="fu">is.na</span><span class="op">(</span><span class="va">comp_df</span><span class="op">$</span><span class="va">logFC.x</span><span class="op">)</span>,<span class="op">]</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">comp_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">logFC.x</span>, <span class="va">logFC.y</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_abline</span><span class="op">(</span>lty <span class="op">=</span> <span class="fl">2</span>, color <span class="op">=</span> <span class="st">"grey"</span><span class="op">)</span> <span class="op">+</span></span>
+<span>    <span class="fu">geom_point</span><span class="op">(</span><span class="op">)</span> </span></code></pre>
 </div>
-<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
-condition, which you can sort of see, especially if you
-<code>log1p()</code> the counts or discard rows that show much higher
-values. ExE ectoderm counts were much higher in samples 8 and 10
-compared to 5, 7, and 9.</p>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb54">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Reshape to long format for ggplot facets. This is 1000x times easier to do</span></span>
+<span><span class="co"># with tidyverse packages:</span></span>
+<span><span class="va">pval_df</span> <span class="op">&lt;-</span> <span class="fu">reshape</span><span class="op">(</span><span class="va">comp_df</span><span class="op">[</span>,<span class="fu">c</span><span class="op">(</span><span class="st">"gene"</span>, <span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">]</span>,</span>
+<span>                   direction <span class="op">=</span> <span class="st">"long"</span>, </span>
+<span>                   v.names <span class="op">=</span> <span class="st">"Pvalue"</span>,</span>
+<span>                   timevar <span class="op">=</span> <span class="st">"pool_factor"</span>,</span>
+<span>                   times <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"with pool factor"</span>, <span class="st">"no pool factor"</span><span class="op">)</span>,</span>
+<span>                   varying <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">pval_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">Pvalue</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_histogram</span><span class="op">(</span>boundary <span class="op">=</span> <span class="fl">0</span>,</span>
+<span>                   bins <span class="op">=</span> <span class="fl">30</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">facet_wrap</span><span class="op">(</span><span class="st">"pool_factor"</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-2.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We can see that in this case, the logFC estimates are strongly
+consistent between the two models, which tells us that the inclusion of
+the <code>pool</code> factor in the model doesn’t strongly influence the
+estimate of the <code>tomato</code> coefficients in this case.</p>
+<p>The p-value histograms both look alright here, with a largely flat
+plateau over most of the 0 - 1 range and a spike near 0. This is
+consistent with the hypothesis that most genes are unaffected by
+<code>tomato</code> but there are a small handful that clearly are.</p>
+<p>If there were large shifts in the logFC estimates or p-value
+distributions, that’s a sign that the design specification change has a
+large impact on how the model sees the data. If that happens, you’ll
+need to think carefully and critically about what variables should and
+should not be included in the model formula.</p>
 </div>
 </div>
 </div>
@@ -7103,8 +7149,8 @@ <h3 class="callout-title">Key Points</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/aio.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/aio.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
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 <p>We see in the help documentation for <code>?clusterCells</code> that
 all of the clustering algorithm details are handled through the
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 <p>You can see that at least among the top markers, cluster 6 (pale
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 <p>The <code>NNGraphParam</code> constructor has an argument
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@@ -3665,7 +3665,7 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
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@@ -3704,7 +3704,7 @@ <h3 class="callout-title">Exercise 2: Reference marker genes</h3>
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 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb47">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -3777,7 +3777,7 @@ <h3 class="callout-title">Extension Challenge 1: Group pair comparisons</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution7" aria-expanded="false" aria-controls="collapseSolution7">
   <h4 class="accordion-header" id="headingSolution7"> Show me the solution </h4>
 </button>
-<div id="collapseSolution7" class="accordion-collapse collapse" aria-labelledby="headingSolution7" data-bs-parent="#accordionSolution7">
+<div id="collapseSolution7" class="accordion-collapse collapse" data-bs-parent="#accordionSolution7" aria-labelledby="headingSolution7">
 <div class="accordion-body">
 <p>One important reason why is because averages over all other clusters
 can be sensitive to the cell type composition. If a rare cell type shows
@@ -3811,7 +3811,7 @@ <h3 class="callout-title">Extension Challenge 2: Parallelizing SingleR</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution8" aria-expanded="false" aria-controls="collapseSolution8">
   <h4 class="accordion-header" id="headingSolution8"> Show me the solution </h4>
 </button>
-<div id="collapseSolution8" class="accordion-collapse collapse" aria-labelledby="headingSolution8" data-bs-parent="#accordionSolution8">
+<div id="collapseSolution8" class="accordion-collapse collapse" data-bs-parent="#accordionSolution8" aria-labelledby="headingSolution8">
 <div class="accordion-body">
 <p>Use <code>BiocParallel</code> and the <code>BPPARAM</code> argument!
 This example will set it to use four cores on your laptop, but you can
@@ -3853,7 +3853,7 @@ <h3 class="callout-title">Extension Challenge 3: Critical inspection of diagnost
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution9" aria-expanded="false" aria-controls="collapseSolution9">
   <h4 class="accordion-header" id="headingSolution9"> Show me the solution </h4>
 </button>
-<div id="collapseSolution9" class="accordion-collapse collapse" aria-labelledby="headingSolution9" data-bs-parent="#accordionSolution9">
+<div id="collapseSolution9" class="accordion-collapse collapse" data-bs-parent="#accordionSolution9" aria-labelledby="headingSolution9">
 <div class="accordion-body">
 <p>The example that jumps out most strongly to the eye is ExE endoderm,
 which doesn’t show clear separate modes. Simultaneously, Endothelium
@@ -3932,7 +3932,7 @@ <h3 class="callout-title">Key Points</h3>
  -->
 </section></section><section id="aio-multi-sample"><p>Content from <a href="multi-sample.html">Multi-sample analyses</a></p>
 <hr>
-<p>Last updated on 2024-10-03 |
+<p>Last updated on 2024-10-04 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 <p>Estimated time: <i aria-hidden="true" data-feather="clock"></i> 45 minutes</p>
@@ -4974,16 +4974,15 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </section><section><h2 class="section-heading" id="exercises">Exercises<a class="anchor" aria-label="anchor" href="#exercises"></a>
 </h2>
 <hr class="half-width">
-<div id="exercise-1-replicates" class="callout challenge">
+<div id="exercise-1-heatmaps" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-1-replicates" class="callout-inner">
-<h3 class="callout-title">Exercise 1: Replicates</h3>
+<div id="exercise-1-heatmaps" class="callout-inner">
+<h3 class="callout-title">Exercise 1: Heatmaps</h3>
 <div class="callout-content">
-<p>Test differential expressed genes with just 2 replicates per
-condition and look into the changes in the results and possible emerging
-issues.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -4994,9 +4993,9 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
-<p>Remember, you can subset SingleCellExperiments with logical indices,
-just like a matrix. You can also access their column data with the
-<code>$</code> accessor, like a data frame.</p>
+<p>You can simply hand <code>pheatmap()</code> a matrix as its only
+argument. <code>pheatmap()</code> has a million options you can tweak,
+but the defaults are usually pretty good.</p>
 </div>
 </div>
 </div>
@@ -5012,29 +5011,27 @@ <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
-<span></span>
-<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
-<span>    <span class="va">summed.filt.subset</span>, </span>
-<span>    label <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
-<span>    design <span class="op">=</span> <span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
-<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
-<span>    condition <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
-<span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
 </div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-24-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-heatmaps" class="callout challenge">
+<div id="exercise-2-model-specification-and-comparison" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-heatmaps" class="callout-inner">
-<h3 class="callout-title">Exercise 2: Heatmaps</h3>
+<div id="exercise-2-model-specification-and-comparison" class="callout-inner">
+<h3 class="callout-title">Exercise 2: Model specification and comparison</h3>
 <div class="callout-content">
-<p>Use the <code>pheatmap</code> package to create a heatmap of the
-abundances table. Does it comport with the model results?</p>
+<p>Try re-running the pseudobulk DGE without the <code>pool</code>
+factor in the design specification. Compare the logFC estimates and the
+distribution of p-values for the <code>Erythroid3</code> cell type.</p>
 </div>
 </div>
 </div>
@@ -5045,9 +5042,10 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" data-bs-parent="#accordionHint2" aria-labelledby="headingHint2">
 <div class="accordion-body">
-<p>You can just hand <code>pheatmap()</code> a matrix as its only
-argument. It has a million options, but the defaults are usually pretty
-good.</p>
+<p>After running the second pseudobulk DGE, you can join the two
+<code>DataFrame</code>s of <code>Erythroid3</code> statistics using the
+<code>merge()</code> function. You will need to create a common key
+column from the gene IDs.</p>
 </div>
 </div>
 </div>
@@ -5063,13 +5061,61 @@ <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="va">de.results2</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
+<span>    <span class="va">summed.filt</span>, </span>
+<span>    label <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design <span class="op">=</span> <span class="op">~</span><span class="va">tomato</span>,</span>
+<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth1</span> <span class="op">&lt;-</span> <span class="va">de.results</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth2</span> <span class="op">&lt;-</span> <span class="va">de.results2</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth1</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth1</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth2</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth2</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="fu">merge</span><span class="op">(</span><span class="va">eryth1</span>, <span class="va">eryth2</span>, by <span class="op">=</span> <span class="st">'gene'</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="va">comp_df</span><span class="op">[</span><span class="op">!</span><span class="fu">is.na</span><span class="op">(</span><span class="va">comp_df</span><span class="op">$</span><span class="va">logFC.x</span><span class="op">)</span>,<span class="op">]</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">comp_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">logFC.x</span>, <span class="va">logFC.y</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_abline</span><span class="op">(</span>lty <span class="op">=</span> <span class="fl">2</span>, color <span class="op">=</span> <span class="st">"grey"</span><span class="op">)</span> <span class="op">+</span></span>
+<span>    <span class="fu">geom_point</span><span class="op">(</span><span class="op">)</span> </span></code></pre>
 </div>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
-condition, which you can sort of see, especially if you
-<code>log1p()</code> the counts or discard rows that show much higher
-values. ExE ectoderm counts were much higher in samples 8 and 10
-compared to 5, 7, and 9.</p>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb54">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Reshape to long format for ggplot facets. This is 1000x times easier to do</span></span>
+<span><span class="co"># with tidyverse packages:</span></span>
+<span><span class="va">pval_df</span> <span class="op">&lt;-</span> <span class="fu">reshape</span><span class="op">(</span><span class="va">comp_df</span><span class="op">[</span>,<span class="fu">c</span><span class="op">(</span><span class="st">"gene"</span>, <span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">]</span>,</span>
+<span>                   direction <span class="op">=</span> <span class="st">"long"</span>, </span>
+<span>                   v.names <span class="op">=</span> <span class="st">"Pvalue"</span>,</span>
+<span>                   timevar <span class="op">=</span> <span class="st">"pool_factor"</span>,</span>
+<span>                   times <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"with pool factor"</span>, <span class="st">"no pool factor"</span><span class="op">)</span>,</span>
+<span>                   varying <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">pval_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">Pvalue</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_histogram</span><span class="op">(</span>boundary <span class="op">=</span> <span class="fl">0</span>,</span>
+<span>                   bins <span class="op">=</span> <span class="fl">30</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">facet_wrap</span><span class="op">(</span><span class="st">"pool_factor"</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-2.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We can see that in this case, the logFC estimates are strongly
+consistent between the two models, which tells us that the inclusion of
+the <code>pool</code> factor in the model doesn’t strongly influence the
+estimate of the <code>tomato</code> coefficients in this case.</p>
+<p>The p-value histograms both look alright here, with a largely flat
+plateau over most of the 0 - 1 range and a spike near 0. This is
+consistent with the hypothesis that most genes are unaffected by
+<code>tomato</code> but there are a small handful that clearly are.</p>
+<p>If there were large shifts in the logFC estimates or p-value
+distributions, that’s a sign that the design specification change has a
+large impact on how the model sees the data. If that happens, you’ll
+need to think carefully and critically about what variables should and
+should not be included in the model formula.</p>
 </div>
 </div>
 </div>
@@ -7111,8 +7157,8 @@ <h3 class="callout-title">Key Points</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/aio.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/aio.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/cell_type_annotation.html b/instructor/cell_type_annotation.html
index 82b3ab0..fc6e1aa 100644
--- a/instructor/cell_type_annotation.html
+++ b/instructor/cell_type_annotation.html
@@ -518,7 +518,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <p>We see in the help documentation for <code>?clusterCells</code> that
 all of the clustering algorithm details are handled through the
@@ -712,7 +712,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <p>You can see that at least among the top markers, cluster 6 (pale
 green) tends to have the least separation from cluster 1.</p>
@@ -1007,7 +1007,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1270,7 +1270,7 @@ <h3 class="callout-title">Challenge</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb43">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1415,7 +1415,7 @@ <h3 class="callout-title">Exercise 1: Clustering</h3>
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>The <code>NNGraphParam</code> constructor has an argument
 <code>cluster.args</code>. This allows to specify arguments passed on to
@@ -1432,7 +1432,7 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
   <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
+<div id="collapseSolution5" class="accordion-collapse collapse" data-bs-parent="#accordionSolution5" aria-labelledby="headingSolution5">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1470,7 +1470,7 @@ <h3 class="callout-title">Exercise 2: Reference marker genes</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution6" aria-expanded="false" aria-controls="collapseSolution6">
   <h4 class="accordion-header" id="headingSolution6"> Show me the solution </h4>
 </button>
-<div id="collapseSolution6" class="accordion-collapse collapse" aria-labelledby="headingSolution6" data-bs-parent="#accordionSolution6">
+<div id="collapseSolution6" class="accordion-collapse collapse" data-bs-parent="#accordionSolution6" aria-labelledby="headingSolution6">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb47">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1543,7 +1543,7 @@ <h3 class="callout-title">Extension Challenge 1: Group pair comparisons</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution7" aria-expanded="false" aria-controls="collapseSolution7">
   <h4 class="accordion-header" id="headingSolution7"> Show me the solution </h4>
 </button>
-<div id="collapseSolution7" class="accordion-collapse collapse" aria-labelledby="headingSolution7" data-bs-parent="#accordionSolution7">
+<div id="collapseSolution7" class="accordion-collapse collapse" data-bs-parent="#accordionSolution7" aria-labelledby="headingSolution7">
 <div class="accordion-body">
 <p>One important reason why is because averages over all other clusters
 can be sensitive to the cell type composition. If a rare cell type shows
@@ -1577,7 +1577,7 @@ <h3 class="callout-title">Extension Challenge 2: Parallelizing SingleR</h3>
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution8" aria-expanded="false" aria-controls="collapseSolution8">
   <h4 class="accordion-header" id="headingSolution8"> Show me the solution </h4>
 </button>
-<div id="collapseSolution8" class="accordion-collapse collapse" aria-labelledby="headingSolution8" data-bs-parent="#accordionSolution8">
+<div id="collapseSolution8" class="accordion-collapse collapse" data-bs-parent="#accordionSolution8" aria-labelledby="headingSolution8">
 <div class="accordion-body">
 <p>Use <code>BiocParallel</code> and the <code>BPPARAM</code> argument!
 This example will set it to use four cores on your laptop, but you can
@@ -1619,7 +1619,7 @@ <h3 class="callout-title">Extension Challenge 3: Critical inspection of diagnost
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution9" aria-expanded="false" aria-controls="collapseSolution9">
   <h4 class="accordion-header" id="headingSolution9"> Show me the solution </h4>
 </button>
-<div id="collapseSolution9" class="accordion-collapse collapse" aria-labelledby="headingSolution9" data-bs-parent="#accordionSolution9">
+<div id="collapseSolution9" class="accordion-collapse collapse" data-bs-parent="#accordionSolution9" aria-labelledby="headingSolution9">
 <div class="accordion-body">
 <p>The example that jumps out most strongly to the eye is ExE endoderm,
 which doesn’t show clear separate modes. Simultaneously, Endothelium
@@ -1751,7 +1751,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/cell_type_annotation.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-02",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/eda_qc.html b/instructor/eda_qc.html
index 73e281a..28c6a89 100644
--- a/instructor/eda_qc.html
+++ b/instructor/eda_qc.html
@@ -1921,7 +1921,7 @@ <h3 class="callout-title">Further Reading</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/eda_qc.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/hca.html b/instructor/hca.html
index 556befe..f95afb1 100644
--- a/instructor/hca.html
+++ b/instructor/hca.html
@@ -992,7 +992,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/hca.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/images.html b/instructor/images.html
index dff2778..961e047 100644
--- a/instructor/images.html
+++ b/instructor/images.html
@@ -454,7 +454,11 @@ <h3 id="multi-sample-figure-6">Figure 6</h3>
 <h3 id="multi-sample-figure-7">Figure 7</h3>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-15-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
 <h3 id="multi-sample-figure-8">Figure 8</h3>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-24-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
+<h3 id="multi-sample-figure-9">Figure 9</h3>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
+<h3 id="multi-sample-figure-10">Figure 10</h3>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-2.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
 <hr class="half-width">
 <h3 id="large_data-figure-1">Figure 1</h3>
 <figure><img src="../fig/large_data-rendered-unnamed-chunk-7-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="hca"><h2 class="section-heading"><a href="hca.html">Accessing data from the Human Cell Atlas (HCA)Single Cell data sources<a class="anchor" aria-label="anchor" href="#single-cell-data-sources"></a></a></h2>
@@ -508,8 +512,8 @@ <h3 id="hca-figure-1">Figure 1</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/images.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/images.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/index.html b/instructor/index.html
index d77c5bb..5c49738 100644
--- a/instructor/index.html
+++ b/instructor/index.html
@@ -457,7 +457,7 @@ <h4 class="accordion-header" id="headingSolution1">
   If you already have R and RStudio installed
   </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <ul><li>Open RStudio, and click on “Help” &gt; “Check for updates”. If a new
 version is available, quit RStudio, and download the latest version for
@@ -483,7 +483,7 @@ <h4 class="accordion-header" id="headingSolution2">
   If you don’t have R and RStudio installed
   </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <ul><li>Download R from the <a href="https://cran.r-project.org/bin/windows/base/release.htm" class="external-link">CRAN
 website</a>.</li>
@@ -514,7 +514,7 @@ <h4 class="accordion-header" id="headingSolution3">
   If you already have R and RStudio installed
   </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <ul><li>Open RStudio, and click on “Help” &gt; “Check for updates”. If a new
 version is available, quit RStudio, and download the latest version for
@@ -538,7 +538,7 @@ <h4 class="accordion-header" id="headingSolution4">
   If you don’t have R and RStudio installed
   </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <ul><li>Download R from the <a href="https://cran.r-project.org/bin/macosx/" class="external-link">CRAN website</a>.</li>
 <li>Select the <code>.pkg</code> file for the latest R version</li>
@@ -571,7 +571,7 @@ <h4 class="accordion-header" id="headingSolution5">
   Install R using your package manager and RStudio
   </h4>
 </button>
-<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
+<div id="collapseSolution5" class="accordion-collapse collapse" data-bs-parent="#accordionSolution5" aria-labelledby="headingSolution5">
 <div class="accordion-body">
 <ul><li>Follow the instructions for your distribution from <a href="https://cloud.r-project.org/bin/linux" class="external-link">CRAN</a>, they provide
 information to get the most recent version of R for common
@@ -693,8 +693,8 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/index.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/index.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/instructor-notes.html b/instructor/instructor-notes.html
index ac70abd..ca23ba6 100644
--- a/instructor/instructor-notes.html
+++ b/instructor/instructor-notes.html
@@ -441,8 +441,8 @@ <h1>Instructor Notes</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/instructor-notes.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/instructor-notes.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/intro-sce.html b/instructor/intro-sce.html
index cba8680..8b414cb 100644
--- a/instructor/intro-sce.html
+++ b/instructor/intro-sce.html
@@ -981,7 +981,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/intro-sce.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-02",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/key-points.html b/instructor/key-points.html
index ed91ed1..273d466 100644
--- a/instructor/key-points.html
+++ b/instructor/key-points.html
@@ -540,8 +540,8 @@ <h2 class="accordion-header" id="flush-headingTwelve">
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/key-points.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/key-points.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/large_data.html b/instructor/large_data.html
index fbb8ead..b7bf583 100644
--- a/instructor/large_data.html
+++ b/instructor/large_data.html
@@ -1619,7 +1619,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/large_data.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-02",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/multi-sample.html b/instructor/multi-sample.html
index c7a5b74..92d94d5 100644
--- a/instructor/multi-sample.html
+++ b/instructor/multi-sample.html
@@ -331,7 +331,7 @@ <h2 class="accordion-header" id="flush-headingTwelve">
       </div>
       <hr></nav><main id="main-content" class="main-content"><div class="container lesson-content">
         <h1>Multi-sample analyses</h1>
-        <p>Last updated on 2024-10-03 |
+        <p>Last updated on 2024-10-04 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 
@@ -1357,16 +1357,15 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 [105] formatR_1.14             </code></pre>
 </div>
 </section><section><h2 class="section-heading" id="exercises">Exercises<a class="anchor" aria-label="anchor" href="#exercises"></a></h2>
-<hr class="half-width"><div id="exercise-1-replicates" class="callout challenge">
+<hr class="half-width"><div id="exercise-1-heatmaps" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-1-replicates" class="callout-inner">
-<h3 class="callout-title">Exercise 1: Replicates</h3>
+<div id="exercise-1-heatmaps" class="callout-inner">
+<h3 class="callout-title">Exercise 1: Heatmaps</h3>
 <div class="callout-content">
-<p>Test differential expressed genes with just 2 replicates per
-condition and look into the changes in the results and possible emerging
-issues.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -1377,9 +1376,9 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
-<p>Remember, you can subset SingleCellExperiments with logical indices,
-just like a matrix. You can also access their column data with the
-<code>$</code> accessor, like a data frame.</p>
+<p>You can simply hand <code>pheatmap()</code> a matrix as its only
+argument. <code>pheatmap()</code> has a million options you can tweak,
+but the defaults are usually pretty good.</p>
 </div>
 </div>
 </div>
@@ -1395,29 +1394,27 @@ <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
-<span></span>
-<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
-<span>    <span class="va">summed.filt.subset</span>, </span>
-<span>    label <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
-<span>    design <span class="op">=</span> <span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
-<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
-<span>    condition <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
-<span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
 </div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-24-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-heatmaps" class="callout challenge">
+<div id="exercise-2-model-specification-and-comparison" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-heatmaps" class="callout-inner">
-<h3 class="callout-title">Exercise 2: Heatmaps</h3>
+<div id="exercise-2-model-specification-and-comparison" class="callout-inner">
+<h3 class="callout-title">Exercise 2: Model specification and comparison</h3>
 <div class="callout-content">
-<p>Use the <code>pheatmap</code> package to create a heatmap of the
-abundances table. Does it comport with the model results?</p>
+<p>Try re-running the pseudobulk DGE without the <code>pool</code>
+factor in the design specification. Compare the logFC estimates and the
+distribution of p-values for the <code>Erythroid3</code> cell type.</p>
 </div>
 </div>
 </div>
@@ -1428,9 +1425,10 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" data-bs-parent="#accordionHint2" aria-labelledby="headingHint2">
 <div class="accordion-body">
-<p>You can just hand <code>pheatmap()</code> a matrix as its only
-argument. It has a million options, but the defaults are usually pretty
-good.</p>
+<p>After running the second pseudobulk DGE, you can join the two
+<code>DataFrame</code>s of <code>Erythroid3</code> statistics using the
+<code>merge()</code> function. You will need to create a common key
+column from the gene IDs.</p>
 </div>
 </div>
 </div>
@@ -1446,13 +1444,61 @@ <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="va">de.results2</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
+<span>    <span class="va">summed.filt</span>, </span>
+<span>    label <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design <span class="op">=</span> <span class="op">~</span><span class="va">tomato</span>,</span>
+<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth1</span> <span class="op">&lt;-</span> <span class="va">de.results</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth2</span> <span class="op">&lt;-</span> <span class="va">de.results2</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth1</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth1</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth2</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth2</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="fu">merge</span><span class="op">(</span><span class="va">eryth1</span>, <span class="va">eryth2</span>, by <span class="op">=</span> <span class="st">'gene'</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="va">comp_df</span><span class="op">[</span><span class="op">!</span><span class="fu">is.na</span><span class="op">(</span><span class="va">comp_df</span><span class="op">$</span><span class="va">logFC.x</span><span class="op">)</span>,<span class="op">]</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">comp_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">logFC.x</span>, <span class="va">logFC.y</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_abline</span><span class="op">(</span>lty <span class="op">=</span> <span class="fl">2</span>, color <span class="op">=</span> <span class="st">"grey"</span><span class="op">)</span> <span class="op">+</span></span>
+<span>    <span class="fu">geom_point</span><span class="op">(</span><span class="op">)</span> </span></code></pre>
 </div>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
-condition, which you can sort of see, especially if you
-<code>log1p()</code> the counts or discard rows that show much higher
-values. ExE ectoderm counts were much higher in samples 8 and 10
-compared to 5, 7, and 9.</p>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb54">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Reshape to long format for ggplot facets. This is 1000x times easier to do</span></span>
+<span><span class="co"># with tidyverse packages:</span></span>
+<span><span class="va">pval_df</span> <span class="op">&lt;-</span> <span class="fu">reshape</span><span class="op">(</span><span class="va">comp_df</span><span class="op">[</span>,<span class="fu">c</span><span class="op">(</span><span class="st">"gene"</span>, <span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">]</span>,</span>
+<span>                   direction <span class="op">=</span> <span class="st">"long"</span>, </span>
+<span>                   v.names <span class="op">=</span> <span class="st">"Pvalue"</span>,</span>
+<span>                   timevar <span class="op">=</span> <span class="st">"pool_factor"</span>,</span>
+<span>                   times <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"with pool factor"</span>, <span class="st">"no pool factor"</span><span class="op">)</span>,</span>
+<span>                   varying <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">pval_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">Pvalue</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_histogram</span><span class="op">(</span>boundary <span class="op">=</span> <span class="fl">0</span>,</span>
+<span>                   bins <span class="op">=</span> <span class="fl">30</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">facet_wrap</span><span class="op">(</span><span class="st">"pool_factor"</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-2.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We can see that in this case, the logFC estimates are strongly
+consistent between the two models, which tells us that the inclusion of
+the <code>pool</code> factor in the model doesn’t strongly influence the
+estimate of the <code>tomato</code> coefficients in this case.</p>
+<p>The p-value histograms both look alright here, with a largely flat
+plateau over most of the 0 - 1 range and a spike near 0. This is
+consistent with the hypothesis that most genes are unaffected by
+<code>tomato</code> but there are a small handful that clearly are.</p>
+<p>If there were large shifts in the logFC estimates or p-value
+distributions, that’s a sign that the design specification change has a
+large impact on how the model sees the data. If that happens, you’ll
+need to think carefully and critically about what variables should and
+should not be included in the model formula.</p>
 </div>
 </div>
 </div>
@@ -1603,8 +1649,8 @@ <h3 class="callout-title">Key Points</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/multi-sample.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/multi-sample.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/profiles.html b/instructor/profiles.html
index c2b3182..48677b4 100644
--- a/instructor/profiles.html
+++ b/instructor/profiles.html
@@ -370,8 +370,8 @@ <h1>Learner Profiles</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/profiles.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/profiles.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/instructor/reference.html b/instructor/reference.html
index 37bb50a..85f4c33 100644
--- a/instructor/reference.html
+++ b/instructor/reference.html
@@ -413,7 +413,7 @@ <h1>Reference</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/reference.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-09-24",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/intro-sce.html b/intro-sce.html
index fec7fa8..7f8a558 100644
--- a/intro-sce.html
+++ b/intro-sce.html
@@ -979,7 +979,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/intro-sce.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-02",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/key-points.html b/key-points.html
index 1cc51fa..4894366 100644
--- a/key-points.html
+++ b/key-points.html
@@ -538,8 +538,8 @@ <h2 class="accordion-header" id="flush-headingTwelve">
   "url": "https://ccb-hms.github.io/osca-carpentries/key-points.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/key-points.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/large_data.html b/large_data.html
index 669d60e..b892e1c 100644
--- a/large_data.html
+++ b/large_data.html
@@ -1617,7 +1617,7 @@ <h3 class="callout-title">Key Points</h3>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/large_data.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-10-02",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/md5sum.txt b/md5sum.txt
index 57111d5..44ccce2 100644
--- a/md5sum.txt
+++ b/md5sum.txt
@@ -7,7 +7,7 @@
 "episodes/intro-sce.Rmd" "b704934867b22d804de1e0fa0a9600eb" "site/built/intro-sce.md" "2024-10-02"
 "episodes/eda_qc.Rmd" "d1a9a8a578fff2b0e9566ec613da388d" "site/built/eda_qc.md" "2024-10-03"
 "episodes/cell_type_annotation.Rmd" "8fab6e0cbb60d6fe6a67a0004c5ce5ab" "site/built/cell_type_annotation.md" "2024-10-02"
-"episodes/multi-sample.Rmd" "f21e7e5dc2ad020ee739374905582225" "site/built/multi-sample.md" "2024-10-03"
+"episodes/multi-sample.Rmd" "6d47bd1941b7a83000873da8d836fba0" "site/built/multi-sample.md" "2024-10-04"
 "episodes/large_data.Rmd" "f19fa53e9e63d4cb8fe0f6ab61c8fc3a" "site/built/large_data.md" "2024-10-02"
 "episodes/hca.Rmd" "247c19cda5e903d2eb1a5dd547d95506" "site/built/hca.md" "2024-10-03"
 "instructors/instructor-notes.md" "205339793f625a1844a768dea8e4a9c8" "site/built/instructor-notes.md" "2024-09-24"
diff --git a/multi-sample.html b/multi-sample.html
index 62be182..a642ecf 100644
--- a/multi-sample.html
+++ b/multi-sample.html
@@ -331,7 +331,7 @@ <h2 class="accordion-header" id="flush-headingTwelve">
       </div>
       <hr></nav><main id="main-content" class="main-content"><div class="container lesson-content">
         <h1>Multi-sample analyses</h1>
-        <p>Last updated on 2024-10-03 |
+        <p>Last updated on 2024-10-04 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 
@@ -1355,16 +1355,15 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 [105] formatR_1.14             </code></pre>
 </div>
 </section><section><h2 class="section-heading" id="exercises">Exercises<a class="anchor" aria-label="anchor" href="#exercises"></a></h2>
-<hr class="half-width"><div id="exercise-1-replicates" class="callout challenge">
+<hr class="half-width"><div id="exercise-1-heatmaps" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-1-replicates" class="callout-inner">
-<h3 class="callout-title">Exercise 1: Replicates</h3>
+<div id="exercise-1-heatmaps" class="callout-inner">
+<h3 class="callout-title">Exercise 1: Heatmaps</h3>
 <div class="callout-content">
-<p>Test differential expressed genes with just 2 replicates per
-condition and look into the changes in the results and possible emerging
-issues.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -1375,9 +1374,9 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
-<p>Remember, you can subset SingleCellExperiments with logical indices,
-just like a matrix. You can also access their column data with the
-<code>$</code> accessor, like a data frame.</p>
+<p>You can simply hand <code>pheatmap()</code> a matrix as its only
+argument. <code>pheatmap()</code> has a million options you can tweak,
+but the defaults are usually pretty good.</p>
 </div>
 </div>
 </div>
@@ -1393,29 +1392,27 @@ <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
-<span></span>
-<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
-<span>    <span class="va">summed.filt.subset</span>, </span>
-<span>    label <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
-<span>    design <span class="op">=</span> <span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
-<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
-<span>    condition <span class="op">=</span> <span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
-<span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
 </div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-24-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-heatmaps" class="callout challenge">
+<div id="exercise-2-model-specification-and-comparison" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-heatmaps" class="callout-inner">
-<h3 class="callout-title">Exercise 2: Heatmaps</h3>
+<div id="exercise-2-model-specification-and-comparison" class="callout-inner">
+<h3 class="callout-title">Exercise 2: Model specification and comparison</h3>
 <div class="callout-content">
-<p>Use the <code>pheatmap</code> package to create a heatmap of the
-abundances table. Does it comport with the model results?</p>
+<p>Try re-running the pseudobulk DGE without the <code>pool</code>
+factor in the design specification. Compare the logFC estimates and the
+distribution of p-values for the <code>Erythroid3</code> cell type.</p>
 </div>
 </div>
 </div>
@@ -1426,9 +1423,10 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" data-bs-parent="#accordionHint2" aria-labelledby="headingHint2">
 <div class="accordion-body">
-<p>You can just hand <code>pheatmap()</code> a matrix as its only
-argument. It has a million options, but the defaults are usually pretty
-good.</p>
+<p>After running the second pseudobulk DGE, you can join the two
+<code>DataFrame</code>s of <code>Erythroid3</code> statistics using the
+<code>merge()</code> function. You will need to create a common key
+column from the gene IDs.</p>
 </div>
 </div>
 </div>
@@ -1444,13 +1442,61 @@ <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+<code class="sourceCode R"><span><span class="va">de.results2</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span></span>
+<span>    <span class="va">summed.filt</span>, </span>
+<span>    label <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design <span class="op">=</span> <span class="op">~</span><span class="va">tomato</span>,</span>
+<span>    coef <span class="op">=</span> <span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition <span class="op">=</span> <span class="va">summed.filt</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth1</span> <span class="op">&lt;-</span> <span class="va">de.results</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth2</span> <span class="op">&lt;-</span> <span class="va">de.results2</span><span class="op">$</span><span class="va">Erythroid3</span></span>
+<span></span>
+<span><span class="va">eryth1</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth1</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">eryth2</span><span class="op">$</span><span class="va">gene</span> <span class="op">&lt;-</span> <span class="fu">rownames</span><span class="op">(</span><span class="va">eryth2</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="fu">merge</span><span class="op">(</span><span class="va">eryth1</span>, <span class="va">eryth2</span>, by <span class="op">=</span> <span class="st">'gene'</span><span class="op">)</span></span>
+<span></span>
+<span><span class="va">comp_df</span> <span class="op">&lt;-</span> <span class="va">comp_df</span><span class="op">[</span><span class="op">!</span><span class="fu">is.na</span><span class="op">(</span><span class="va">comp_df</span><span class="op">$</span><span class="va">logFC.x</span><span class="op">)</span>,<span class="op">]</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">comp_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">logFC.x</span>, <span class="va">logFC.y</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_abline</span><span class="op">(</span>lty <span class="op">=</span> <span class="fl">2</span>, color <span class="op">=</span> <span class="st">"grey"</span><span class="op">)</span> <span class="op">+</span></span>
+<span>    <span class="fu">geom_point</span><span class="op">(</span><span class="op">)</span> </span></code></pre>
 </div>
-<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
-condition, which you can sort of see, especially if you
-<code>log1p()</code> the counts or discard rows that show much higher
-values. ExE ectoderm counts were much higher in samples 8 and 10
-compared to 5, 7, and 9.</p>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb54">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="co"># Reshape to long format for ggplot facets. This is 1000x times easier to do</span></span>
+<span><span class="co"># with tidyverse packages:</span></span>
+<span><span class="va">pval_df</span> <span class="op">&lt;-</span> <span class="fu">reshape</span><span class="op">(</span><span class="va">comp_df</span><span class="op">[</span>,<span class="fu">c</span><span class="op">(</span><span class="st">"gene"</span>, <span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">]</span>,</span>
+<span>                   direction <span class="op">=</span> <span class="st">"long"</span>, </span>
+<span>                   v.names <span class="op">=</span> <span class="st">"Pvalue"</span>,</span>
+<span>                   timevar <span class="op">=</span> <span class="st">"pool_factor"</span>,</span>
+<span>                   times <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"with pool factor"</span>, <span class="st">"no pool factor"</span><span class="op">)</span>,</span>
+<span>                   varying <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="st">"PValue.x"</span>, <span class="st">"PValue.y"</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">ggplot</span><span class="op">(</span><span class="va">pval_df</span>, <span class="fu">aes</span><span class="op">(</span><span class="va">Pvalue</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">geom_histogram</span><span class="op">(</span>boundary <span class="op">=</span> <span class="fl">0</span>,</span>
+<span>                   bins <span class="op">=</span> <span class="fl">30</span><span class="op">)</span> <span class="op">+</span> </span>
+<span>    <span class="fu">facet_wrap</span><span class="op">(</span><span class="st">"pool_factor"</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-2.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We can see that in this case, the logFC estimates are strongly
+consistent between the two models, which tells us that the inclusion of
+the <code>pool</code> factor in the model doesn’t strongly influence the
+estimate of the <code>tomato</code> coefficients in this case.</p>
+<p>The p-value histograms both look alright here, with a largely flat
+plateau over most of the 0 - 1 range and a spike near 0. This is
+consistent with the hypothesis that most genes are unaffected by
+<code>tomato</code> but there are a small handful that clearly are.</p>
+<p>If there were large shifts in the logFC estimates or p-value
+distributions, that’s a sign that the design specification change has a
+large impact on how the model sees the data. If that happens, you’ll
+need to think carefully and critically about what variables should and
+should not be included in the model formula.</p>
 </div>
 </div>
 </div>
@@ -1601,8 +1647,8 @@ <h3 class="callout-title">Key Points</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/multi-sample.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/multi-sample.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/pkgdown.yml b/pkgdown.yml
index ec6e369..f806651 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -2,4 +2,4 @@ pandoc: 3.1.11
 pkgdown: 2.1.1
 pkgdown_sha: ~
 articles: {}
-last_built: 2024-10-03T16:38Z
+last_built: 2024-10-04T16:55Z
diff --git a/profiles.html b/profiles.html
index 62e5963..61f9e82 100644
--- a/profiles.html
+++ b/profiles.html
@@ -370,8 +370,8 @@ <h1>Learner Profiles</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/profiles.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/profiles.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-10-03",
-  "datePublished": "2024-10-03"
+  "dateModified": "2024-10-04",
+  "datePublished": "2024-10-04"
 }
 
   </script><script>
diff --git a/reference.html b/reference.html
index 30a57dc..9b3ac60 100644
--- a/reference.html
+++ b/reference.html
@@ -411,7 +411,7 @@ <h1>Reference</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/reference.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-09-24",
-  "datePublished": "2024-10-03"
+  "datePublished": "2024-10-04"
 }
 
   </script><script>